i^^:S E :2 41235 ) DEVELOPMENT OF ULTBASONIC
METHODS FOB HEHODT NAHIC MEASUREMENTS
Progress Heport (Colorado State Dniv.)
115 p HC $5.25 CSCL C6D
G3/52
N 75- 17084'
Onclas
10233 )
DEVELOPMENT OF ULTRASONIC METHODS FOR
HEMODYNAMIC MEASUREMENTS
by
M. B. HISTAND* C. W. MILLER*
M. K. WELLS F. D. MCLEOD
E. R. GREENE D. WINTER
From the Departments of
Mechanical Engineering and Physiology and Biophysics
COLORADO STATE UNIVERSITY
FORT COLLINS, COLORADO 80523
A Semi-annual Progress Report Prepared for the
National Aeronautics and Space Administration
Under NASA GRANT NSG-2009
February 1, 1975
♦Principal Investigators
i
TABLE OF CONTENTS
I. Introduction
II. Volume Flow Measurement Technique
III. Implant and Transcutaneous Velocity and Flow Comparisons
IV. Half Power Diameter Measurements
V. Wide Gate Full Vessel Illumination
VI. Ultrasound Dosimetry
VII. Spectral Analysis of Pulse Doppler Signals Using Sonograms
VIII. Performance of the Pulsed Doppler Velocity Meter
IX. Performance of the NASA-PUDVM
X. Standard Test System
XI. Bibliography
XII. Appendix I
XIII. Appendix II
-3-
I. Introduction
This progress report summarizes the results of our research in
diagnostic ultrasound conducted during August 1974 - January 1975.
The major items to which the report will be addressed are:
A. Based on state of the art Doppler ultrasound instrumentation,
a transcutaneous method to measure instantaneous mean blood flow in
peripheral arteries of man is defined. Problems toward which further
research will be directed prior to construction of the final instrumen-
tation package are discussed.
B. A detailed evaluation of transcutaneous and implanted cuff
ultrasound velocity measurements was completed. Using our conventional
narrow gate scan with the PUDVM the accuracies of velocity, flow, and
diameter measurements were assessed for steady fiow in rigid tubes,
bovine carotid segments, dialysis tubing, and for pulsatile flow, in
anesthetized dogs.
C. The analysis of the backscattered power was undertaken to
determine the accuracy of transmural diameter measurements by the half
power method.
D. The wide gate-full illumination method of measuring instantaneous
mean velocity was assessed in steady flow for the dialysis tube and for
pulsatile flow in the dog.
£. The performance criteria of the PUDVM were described, A
spectrum analyzer and FFT digital program were used to examine the
spectral characteristics of the Doppler signals as a function of
Reynold's number.
F. The performance of the NASA-PUDVM was assessed.
G. A standard transducer test system was designed and evaluated.
PRECEDING PAGE BLANK NOT ITLME0
- 4 -
H. Ultrasound dosimetry procedures were investigated.
I. Spectral analysis of the PUDVM signals was performed
using a sonogram.
-5-
II. Volume Flow Measurement Technique
The primary objective of this research project is the definition
and preliminary evaluation of a transcutaneous method for the measurement
of instantaneous mean flow in the peripheral arteries of an animal
or human. The effort is directed toward the eventual development of
ultrasound instrumentation that can be easily applied for the quantitative
measurement of flow in a subcutaneous vessel. State of the art
instrumentation is used. With an emphasis for the method based on
ease of application and accuracy, we have examined the various possibilities
using state of the art Doppler instrumentation to accomplish this goal.
The theoretical analysis of resolution, methodology, and three methods
for volume flow measurement were described in the progress report
submitted in July, 1974. Based upon this report and further developmental
studies both in simulated blood flow systems (steady flow in dialysis tubes)
and in special animal preparations (chronic implantation of flow cuffs),
we have defined a method based upon current state of the art instrumen-
tation for the measurement of mean flow.
A. Uniform illumination method
Mean instanteous flow will be computed from the product of the
mean instantaneous velocity obtained from the first moment of the Doppler
power spectrum from a wide gate encompassing the entire vessel diameter
and the cross-sectional area obtained from a half power diameter
measurement. The method will combine the measurement of instantaneous
mean velocity using a piezoelectric crystal larger than the vessel
diameter which will uniformly illuminate the cross-section of the
vessel at a specific location with a PUDVM gate opened to enclose the
near wall and far wall. Coupled with this measurement the geometry
- 6 -
of the vessel will be obtained from a small crystal, narrow gate PUDVM
scan to obtain the half power points and thus the vessel diameter.
We ultimately envision a digital display of the computed flow.
An important facet of the method is the design of a transducer
which can be easily positioned on the skin for Doppler angle determination
and velocity measurement. Our preliminary design is shown in Figure 1.
Rectangular piezoelectric crystals will be placed at (1), (2), (3), (4),
(5) permitting angle determinations at a variety of depths (shown). By
rotating the transducer about its axis and using e.g. crystal (1) as
a transmitter and crystal (2) as a receiver the returned signal can be
nulled and thus the normal to the flow axis determined. In the dialysis
flow system the accuracy is ± .5°. The design of the holder will be
based upon the movable protractor designs we have developed for trans-
cutaneous narrow gate scans. The transducer will be positioned by
audio recognition of the signal.
We have carefully examined the wide gate method for determining
mean velocity and are convinced the accuracy is high for Reynolds
numbers above 1500. Further study of flow in the laminar region
(parabolic profiles) is to be conducted. See Section IV. In addition,
the power scan method (Section III) has proven to be an effective
means for measuring diameter on the dialysis tube although we have
problems resolving the far wall in the animal. Since some discrepancies
exist in measuring diameter by the half power method we will devote a
major effort to perfect this method. Low pass filtering will be tried
as an alternative to locate the walls.
- 8 -
III. Implant and Transcutaneous Velocity and Flow Comparisons
Detailed tests have been conducted on dialysis, rigid tube, and
bovine carotid arterial simulation systems. In these systems the
conventional narrow gate scan method that has been utilized in our
laboratory for the last two years was carefully evaluated. Although
errors exist in volume flow calculation by the narrow gate method,
this method can serve as a means of evaluating the correlation between
transcutaneous flow measurements and those made with a cuff implanted
on the vessel. Since we are seeking an accurate and simple method
to measure mean flow, we have not assessed corrections for boundary
errors and truncation as discussed in the previous report. We plan
to look at these errors during 1975.
A. Narrow gate fluid system experiments
Narrow gate scan flow measurements were taken in three types
of vessels: rigid tube, bovine graft, and dialysis tubing. Data
presented in Tables 1 and 2 were taken only under the following
instrument settings and experimental procedures.
Instrument Setting
PUDVM #2
PW 8 cycles
PR 2 (nominally 20 kc)
Gate 1 psec
Transducer #116 2.8 mm crystal
All data was recorded on magnetic tape, digitized and processed
by the digital computer. Since the flow system was steady (nonpulsatile) ,
the peak and average values were similar. The average values were compared
to collection measurements for the rigid tube and bovine graft systems.
-9-
TABLE 1
Flowrate Measured (Q m ) vs. Flowrate PUDVM (Qpg )
Type Vessel Dimensions
Re
Qm cc/sec
Qpncc/sec
Avg.
. Erjor
Rigid Tube ll.Onm ID
740
6.50
3.51
- 45
13.0mm 00
800
7.00
3.88
-44
crystal/ID ratio .255
1030
9.00
5.71
- 37
1150
10.00
6.80
-32
1320
11.50
7.42
8.09
— 30
8.68
7.84
8.42
1490
13.00
11.85
- 8
1600
14.65
13.47
13.06
- 10
12.65
1830
16.00
12.79
17.92 :
15.36
- 4
2290
20.00
19.05
-5
*
2600
22.70
25.68
22.99
24.34
+ 7
2860
25.00
23.14
- 7
3040
26.20
25.62
25.07
* 4
- 24.52
3600
31.40
33.56
+ 7
5200
45.80
41.67
44.09
42.88
- 6
7500
65.40
82.23
79.46
80.84
+ 27
Bovine Graft 7.7mm ID
2500
15.00
14.77
14.88
14.82
- 1
10.0mm OD
5000
30.00
32. 55
32.38
+ 8
crystal/ID ratio .365
33.31
33.05
30.63
5800
35.00
29.95
31.37
30.66
- 12
-iq-
table 2
Type Vessel Dimensions
Dialysis Tubing 6.3 nra 10
crystal/IO ratio .455
7.2 mm ID
crystal/ID ratio .390
Re
Avg.
I
1000
4.73
3.38
3.68
3.53
- 34
1500
7.10
4.68
4.56
4.62
-35
2000
9.46
7.08
7.66
7.32
-23
2500
11.83
8.52
9.02
8.77
- 25
3000
14.19
13.32
14.00
13.66
- 4
3500
16.56
13.77
15.26
14.52
- 12
4000
18.92
14.82
16.10
15.46
- IB
4500
21.30
16.91
17.86
17.39
- 16
5000
23.60
17.16
19.55
18.36
- 22
1000
5.65
3.42
3.72
3.57
- 37
1500
8.48
8.48
8.48
6.12
5.48
6.30
6.37
6.14
6.53
6.16
- 27
2000
11.30
7.82
8.33
8.07
- 28 .
2500
14.13
10.05
12.15
11.10
- 21
3000
16.80
16.80
15.76
15.98
16.02
16.80
16.14
- 4
3500
19.80
16.00
18.70
18.35
- 7
4000
i
22.60
20.95
20.98
20.97
- 7
4500
25.40
22.34
22.88 1 >
22.51 -
' 11
5000
28.35
23.34
24.25
23.80 - 16
i
- 11 -
A rotometer (± 5 % calibration to collection) was used as a standard
during the dialysis tube study. The comparisons would help determine
the ability of the narrow gate scan and developed velocity profile
integration technique for flow rate determination.
Results from the tables suggest the following:
a. Standard and Doppler flow rates compare optimally only within
certain observed Reynolds number values for each vessel type.
Re 1500-5000 rigid tube
Re 3000-4500 7.2 dialysis tubing
Re 3000-4500 6.3 dialysis tubing
Re <2500 -5000 Bovine graft
b. As the tubing diameter increases (crystal diameter/ID ratio
decreases) flow rates obtained from the PUDVM approach the standard
values; within 101.
c. Flow rates determined by the PUDVM for flow regimes of
relatively low Re value (<2000) greatly differ from collection or
rotometer values.
B. Narrow gate comparisons of velocity and flow in the dog
We have conducted extensive tests to compare the measured velocity
and flow parameters obtained on subcutaneous arteries using implanted
Doppler ultrasonic cuffs and transcutaneous probes. The dog was
surgically implanted with ultrasonic cuffs on the right and left femoral
arteries, the abdominal aorta, and the carotid artery. The carotid
artery was surgically exteriorized for ease of transcutaneous recording.
Post mortum exam will indicate whether the artery under these circum-
stances is straight and uniform. Generally, we find that the trans-
cutaneous and cuff narrow gate velocity and flow scans compare favorably
when the Doppler angle is obtained accurately. Table 3 summarizes the
- 12 -
TABLE 3
Narrow gate measurements of diameter, flow and velocity
transcutaneous and cuff
TYPE
NASA DOG 15689
XCUT vs. CUFF
Right Carotid
NUMBER OF
SAMPLES
DIA mm
Diameter
Xcut
N=7
4.18±.03,
4.20±.10*
(mm)
Cuff
N=ll
Average Flow
(cm 3 s J )
Xcut
N=4
2 .62+. 02 ,
2.58±.1(T
Cuff
N=5
Cuff
N=5
2.96±.09
Xcut
N=2
2.37±.00
PEAK
Xcut
N=4
112.5±10.1
\ .
(cms J )
Cuff
N=5
107. 8± 7.2
Cuff
N=6
75.U22.3
Xcut
N=5
91.1±10.7
Notes: PD #2
Cuff
ID 5.0 mm crystal 2.5 mm
PW 8 Xcut Xducer crystal 2.8 mm
PRF 2,3 All data taken during anesthetic
Gate 1 ysec RMS reading 0.15 V
All H.R.
102<HR<128
128<HR<137
141 <HR<143
102<HR<128
128<HR<137
141 <HR<143
For delays of 1 ysec or .5 ysec the data is similar
-13-
results of the experiments with the animal. We will concentrate on
measurements from the right carotid artery although recordings from
the abdominal and femoral arteries confirm what we have found on this
particular artery. For heart rates in the range of 100 to 130 the
centerline peak velocity measured with the PUDVM for the transcutaneous
and the implanted cuff compares within the first standard deviation.
Normally, the centerline peak velocities are approximately 100 cm/sec
and we see for averages of approximately 5 experiments that the transcu-
taneous value was 112 and the value measured with the implanted
cuff at a location 1cm proximal to the transcutaneous measurements
location was 107 cm/second. As the heart rate increases there is
greater variability both In the waveforms and the resulting velocity
values for cuff and the transcutaneous method. By integrating the
velocity profiles, one can obtain the average flow, and again for
a heart rate of 100 to 130 per second the average flow for the
transcutaneous was 2.62 and for the cuff 2.58 cm 3 /sec showing good
agreement between the two methods. For higher heart rates there is
more divergence in the measurements made with the two methods.
Finally, the diameters calculated from velocity profiles show very
close agreement for the transcutaneous and the implanted cuff. Diameters
at the specific locations were approximately 4,2 mm.
The purpose of these experiments was to compare the two methods.
We are not implying that the narrow gate method is the most accurate
means of measuring diameter, flow or centerline peak velocity. However,
these studies do demonstrate the high degree of correlation between
transcutaneous measurements and implanted cuff measurements; necessary
criteria for supporting our contention that transcutaneous measurements
-14-
of velocity and flow can be obtained with a high degree of accuracy.
Figures 2, 3, 4, show the velocity waveforms, velocity profiles,
and average flow waveforms from the implanted cuff on the carotid
artery. Figures 5, 6, 7 show comparable data obtained with a 2.8 mm
transcutaneous probe positioned 1 cm distal to the cuff.
x
PEAK AVC
VELOCITY set NO. 8
NASA DOG
15689
11-22-74
ANES POTX 2.5
CUFF YB CAR 2.5MM
(Jl
t
1 1
i 1 i 1 i
> 1 i
i t i
j
«
•
«
»
•
o
o
o
o
O
o
o
m
o>
in
o
in
o
ho
^3
*^3
in
in
CO
ULLISECONOS
RECORDED FROM THE
distance: IN MM
FIGURE 3, PEAK FORWARD, AVERAGE AND PEAK REVERSE PROFILES
RECORDED FROM THE CUFF.
FIGURE 4. AVERAGE FLOW RECORDED WITH ThE CUFF.
velocity in cm/sec
120 .
PEAK AVC. VELOCITY SET NO. 14
\ NASA DOG
15689
11-22-74
ANES POTX 2.5
XCUT CAR MBH
- 10 .
TIME IN MILLISECONDS
DATA AS SHOWN IN FIGURE 2 EXCEPT RECORDED
TRANSCUTANEOUSLY. NOTE HIGH DEGREE OF CORRELATION WITH
FIGURE 2.
distance in mm
FIGURE 6. TRANSCUTANEOUS VELOCITY PROFILE. COMPARE WITH
FIGURE 3.
o
o
NO
£ IN MILL IS
>US MEAN FLOI
- 21 -
IV, Half Power Diameter Measurements
We propose that the geometry (diameter) of the blood vessel can
be accurately measured by a power scan with a small >.50R transducer .
The first approach to the assessment of this method involves half
power measurements of diameter on dialysis tubes of known diameter.
Results are summarized in Table 4.
A. Dialysis Tube Results
For a 7.7 mm tube measured diameters were ~ 7.5 mm with a 2>8 mm
crysta1 & = -36 ) and 7-65 with a 5-5 mm crystal ^O iEu Fe ~ = ' 71 ^
These errors would reduce the true volume flow measurement by ~ 10%.
Figure 8 displays a power scan of the dialysis tube. For vessels of
' 4 mm diameter or less problems arise: the half power diameters
are approximately 25% too small presumedly due to the curvature of the
vessel and the large crystal. This is inconsistent with the half
power measurements made with 5-8 mm crystals which result in a 10%
over estimate of diameter in a 7 mm tube. We are currently trying
to resolve this problem by considering low pass filtering of the audio
spectrum. Therefore, a more detailed and systematic approach will
be taken. Our conclusion is that the half power method is the simplest
and most accurate method for transcutaneous diameter determination
for vessels whose diameter is > 7 mm.
B. Reiteration of errors in half power measurements
Ambiguity in finding the half power points is limited by four
factors:
1) Ambient Noise . The quality of the power scan is affected
by the Doppler signal to noise ratio (S/N). Both base line shifts
and signal variance are present with poor S/N. In practice this is not
- 22 -
a problem, however, when S/N ratios on the order of 20 to 50 dB
are obtained.
2) Wall motion and wall motion "noise." Wall motion tends to
"blur" the wall location during the power scan, thus a mean diameter
is obtained. While the "blurring" is reduced by multichannel operation
it is not completely eliminated because of the finite integration
time required to measure the signal power (Rayleigh signal statistics
and fading must be integrated out). Large amplitude low frequency
echoes from the wall are another wall motion problem. These echoes
tend to distort the sample function near the wall and make it appear
compressed. This problem is reduced by high pass filtering to
eliminate the echoes. Alternately, low pass filtering can be used to
select or enhance the wall echo and provide an impulse response at
the wall. We plan to examine the latter to determine its accuracy
in the diameter estimation.
3) Range attenuation . The Doppler signal power falls off as
a function of range, tending to obscure the step function endpoint.
This difficulty can be eliminated either by range gain compensation,
proper transducer design, or graphical correction of the power scan
record. See actual data from dog experiments.
4) A fourth and perhaps minor limitation is vessel curvature at
the wall. The step function concept was developed for a plane or
nearly flat surface, however, a vessel wall is a curved surface.
This curvature A, is easily shown to be
where a is the transducer beam diameter and r is the vessel radius.
Evaluation of this for a transducer diameter of .25r leads to a
-23-
curvature of less than 1%.
Combination of the above limitations leads to an experimental
wall location error on the order of 1/4 sample function length and
a diameter error on the order of times the sample function
length. In practical terms the sample function length is on the
order of 1 mm, thus vessel diameter measurement is on the order of
± .44 mm. Although seemingly precise, this is still a 10% error on
a 4 mm vessel .
C. Half Power measurements on blood vessels
Using implanted cuffs and transcutaneous probes we have recorded
rms power scans on the abdominal aorta and carotid arteries. Consistent
with our findings in the dialysis tube, the abdominal aorta values are
accurate but the carotid diameters appear ~ 25% too small. Figure 9
exhibits power scans for the abdominal aorta. Note the range attenuation
which necessitates interpolating a half power point at the far wall.
Transcutaneous measurements produce significant power fluctuations
at the far wall (wall motion} which may obscure the half power points.
Low pass filtering may alleviate this problem. Figure 10 exhibits
power scans for the carotid artery producing diameters of ~ 3.45 mm
which we believe to be too small. Our previous measurements of
carotid inside diameters by surgical exposure result in values of
- 4 mm. Therefore, we must be cautious in using the half power method
of diameter determination In vessels less than 7 mm in diameter.
Table 5 exhibits data on half power diameters for the carotid
and abdominal aorta. The diameters for the carotid should be - 4 mm.
The diameter for the abdominal aorta is quite close to the expected
value.
-24-
TABLE 4
Half Power Diameter Measurement
TRANSDUCER
i
Dialysis Tube
DIAMETERS (MM)
RATIO OF CRYSTAL DIAMETER
TO VESSEL DIAMETER
#116-EC65
7.47
7.55 7.47
.36
2.8 mm
LTZ 5
5.5 mm
7.55
7.71
.71
LTZ 5
8.0 mm
8.20 8.61 8.60
(7 . 88( Rel 500) )
1.03
EC65
8.69
8.70
.71
5.5 mm
EC65
8.69
8.53 8,93
1.03
8.0 m
Notes:
PD #2
PW8
PRF 2
Gate 1
ysec
Tubing OD 7.8 mm
Tubing ID 7.7 mm
Re 3000
i
OTSI 9V
-28-
TABLE 5
1/2 Power Diameters
NASA DOG 15689
RATIO OF CRYSTAL DIAMETER
TRANSDUCER
TO VESSEL DIAMETER
TECHNIQUE
DIAMETERS
RT CAR
#116
.73
Xcut
2.40
RT CAR
NASA
LTZ 5.5
1.44
Xcut
2.65
RT CAR
NASA
LTZ 7.0
1.84
Xcut
2.00 2.40
RT CAR
R. C. Cuff
.65
Potx 5.0
2.60
YB 2.5
Cuff
RT CAR
R. C. Cuff
.65
Potx 2.5
2.70
YB 2.5
Cuff
2.70 2.65
Notes :
PD#2
RMS .15 V
Vessel Diam Assumed 3.8 mm ID
PW8 Delay At 1/2 usee, 1 psec
PRF 2.3
Gate 1 ysec
C=1 . 5x105 cm/sec
-29-
V. Wide Gate Full Vessel Illumination
A rectangular 2 mm by 10 mm transducer was fabricated from LTZ 2
to assess to accuracy of the wide gate full illumination method to
measure mean velocity in a vessel. Presently, the zero crosser
has been used for signal processing although we calculate an error
as great as 15% may occur in determining the first moment of the
power spectrum. Our preliminary findings in the dialysis tube steady
flow system are quite encouraging. As shown in Table 6, we have
obtained results with large circular crystals and two different large
rectangular crystals, one of LTZ 5 and one of LTZ 2. By far the best
results are obtained with the LTZ 2 indicating errors in measurement
of the mean velocity in the range of Reynolds number from 2000 to
5000 are less than 7%. At the very low Reynolds numbers larger errors
occur which merit further investigation. We cannot adequately explain
the reason that larger errors occur with certain piezoelectric
materials, and further investigation is going to be conducted in
transducer design and fabrication in order to optimize the results.
Figures 11 » 12, and 13 exhibit the power spectra obtained with the
LTZ 2 wide gate transducer. For a wide gate measurement one would
expect a nearly rectangular power spectrum and we are obtaining very
close approximations to that under these circumstances. We find also
that the zero crosser is a much better than expected signal processor
for signals using these spectra implying that more sophisticated
signal processing may not be necessary. However, we plan to further
investigate the use of first moment and zero crosser offset processing
of these signals to see if the accuracy can be further improved.
-30-
TABLE 6
COMPARISON V pD vs. Vm fn(Re)
TRANSDUCER NASA LTZ 8.0 mm
NASA EC65 8.0 mm
NASA LTZ 5
Re Vp D (cm/sec) Vm (cm/sec) % difference from standard
(i)
(2)
(3)
(4)
(2)
(1)
(i)
(2)
(3)
1000
15.72
17.3
18.6
18.5
13.42
13.16
19
28.9
38.6
1500
22.26
25.1
28.2
26.0
20.14
19.74
13
24.6
40.0
2000
28.16
30.9
36.7
31.1
26.83
26.32
7
15.2
36.8
2500
33.31
36.9
42.2
34.5
33.55
32.90
1
10.0
25.8
3000
40.22
42.7
47.7
40.5
40.25
39.48
1
6.1
18.5
3500
45.75
48.5
55.1
45.5
46.97
46.06
-1
3.2
17.3
4000
51.48
53.9
61.2
50.0
53.69
52.64
-2
0.4
13.9
4500
56.45
60,0
67.3
57.1
60.40
59.22
-5
0.7
11.4
5000
61.58
65.8'
73.4
61.7
67.10
65.80
-7
1.9
09.4
Full Vessel Ilium
(i)
NASA LTZ 2 rectangle (2 mm X 10 mm)
PW8
(2)
NASA LTZ 8.00 mm 21 Jan (circular)
PD2
(3)
NASA EC65 8.00 mm 23 Jan (circular)
PR2
GN1.0
Gate 18.0 psec
(4)
NASA LTZ 5 rectangle (2 mm X 10 mm)
Power ,15V
Delay 8 usee
7.5 mm dialysis
.
-34-
VI. Ultrasound Dosimetry
Preliminary efforts have been made to document the power
levels emitted by the pulsed ultrasonic Doppler velocity detector.
The first experiment was conducted at the Colorado Medical Center
in Dr. Paul Carson's laboratory (February 14, 1975). The setup
consisted of determining the force exerted by the emitted pulse
upon a highly absorbable buffer plate (SOAB). This force was
determined using an electro-balance (Cahn). The initial results
indicate that the pulse Doppler when operated at the highest
pulse repetition rate (40kc) and longest pulse width (16 cycles)
emits a sound beam which averages a power level of 296 MW/CM 2 .
In these studies a 2,8 mm circular transducer was employed.
If a 25 % insertion factor is assumed for tissue, the result is
a power level of approximately 75 MW/ CM 2 . Peak intensity equals
4.9 W/CM 2 . More work is planned in the future to document the
power levels emitted by such devices as the pulsed ultrasonic
Doppler velocity detector. We feel that intelligent use of
ultrasonic flowmeters demands that continual knowledge of the ultra-
sound dosage be at hand.
-35-
VII. Spectral Analysis of Pulse Doppler Signals Using Sonograms
In an attempt to find the best method for determining the
average blood flow rate in an artery, we have performed analyses
of the Doppler shifted signal using sonograms. The data display
consists of the time varying audio signal displayed at varying
levels of amplitude {each different intensity of the contour
represents a 6 db change). This technique permits display of
the spectral patterns of the signal and from the graph, the various
velocity components within the return Doppler shifted signal are
easily viewed.
This report will present the initial results using this
technique and will suggest future directions. Sonograms were
made for the Doppler shifted signals from an implanted flow cuff
around the abdominal aorta of a dog (2.8 mm transducer). Two
types of sonograms were made from the Doppler shifted signal at
locations across the flow stream by approximate range gating and
by using a wide gate which encompassed the entire flow stream.
These results will be compared with the zero crosser output
(wide gate, scan, and computer calculated).
Figure 13A depicts a sonogram showing the Doppler shifted
information received with a wide gate. The peak velocity recorded
across the flow stream is approximately 101 cm/sec if the lowest
amplitude signal is used. By selecting velocity components of
higher contour intensities (continuous contours) values of 94 and
91 cm/sec result. The entire velocity data for all combinations
are shown in Table 7.
-36-
TABLE 7
Blood velocity values (cm/sec) measured using wide and narrow gate
pulse Doppler options on the abdominal aorta of a dog.
Wide Gate
Zero Crosser
V Peak V
73 19,8
Sonogram
V Peak V
101,94,91 37.4
Zero Crosser
V Peak at C
81 x
Narrow Gate
Sonogram
@centerl ine
V peak
95
Computer Calculated
from profiles
V peak V
42 12.2
The table shows for the wide gate the average velocity at
peak systole as claculated from the zero crosser and sonogram outputs.
The average velocity is similarly listed. The narrow gate measure-
ments for the peak velocity at the flow stream centerline are
also depicted for both the sonogram and zero crosser and finally,
the standard method of profile integration produces the average
peak velocity and the mean velocity. These data show that by
using a narrow sound beam that obviously a large portion of the
velocity information which exists towards to vessel walls will not
be detected using the zero crosser and wide gate. The result is
a higher than actual recorded blood velocity when using the zero
crosser. The sonogram whether using a wide gate or narrow gate Q
produces approximately the same velocity and is close to the peak
velocity measured with a narrow gate zero crosser method. The
reason the wide gate zero crosser and sonogram methods produce
-37-
a higher mean velocity than actual is obviously due to the narrow
sound beam. The discrepancy between the zero crosser and sono-
gram is due to the faulty method of obtaining the mean velocity
by integrating the sonogram. No weighting of the various amplitudes
of the signal were attempted.
We believe that an alternative method for computing the mean
velocity of blood in a superficial vessel may involve the use
of a large transducer and a wide gate pulsed Doppler or even
continuous wave Doppler coupled with sonogram analysis. A
possible valuable approach to attempt would be to compare this
approach to the actual blood velocity. Account must be taken of
the varying signal amplitudes (1st moment analysis) but the sonograms
offer that possibility. Sonogram analysis also offers an alterna-
tive method to the zero crosser for detecting the local velocities
across a flow stream. Figure 13B, for example, shows a sonogram
for the velocity signal recorded at the centerline. It is inter-
esting to note that a relatively narrow band signal occurs during
systole in contrast to the situation using a wide gate where a
wide range of spectra exist. Similarly, at the vessel walls, this
narrow amplitude band disappears (Figure 13C). Presumably the
vessel wall is a major influence in the pattern - both due to
its influence upon flow and the fact that the vessel wall moves in
and out of the sample volume.
VELOCITY (cm/sec)
NARROW GATE NEAR WALL
FIGURE 13a. SONOGRAM PRODUCED WITH THE PULSE DOPPLER IN THE WIDE GATE MODE
FROM A FLOW CUFF ON THE ABDOMINAL AORTA OF A DOG.
VELOCITY (cm/sec)
NARROW , GATE AT £
FIGURE 13b, SONOGRAM PRODUCED WITH A NARROW GATE FROM THE CENTERLINE OF ThE
FLOW STREAM IN A DOG IMPLANTED WITH A FLOW CUFF ON THE ABDOMINAL AORTA.
VELOCITY (cm/sec)
WIDE GATE
IOO
50
0
FIGURE 13c. SONOGRAM PRODUCED WITH A NARROW GATE FROM A PORTION OF THE
FLOW STREAM NEAR THE WALL OF THE ABDOMINAL AORTA IN A DOG IMPLANTED WITh
A FLOW CUFF ON THE ABDOMINAL AORTA.
i
-41-
VIII. Performance of the Pulsed Doppler Velocity Meter
A. Objectives
The objective of this phase of the research program was an
evaluation of the PUDVM for laminar' and turbulent flow measurements.
Previous studies from this laboratory (1) reported on the effects of
emission pulse length, transducer and ultrasound receiver bandwidth,
and sample gate duration on the length of the PUDVM sample function.
The effects of these individual parameters on the measured velocity
profiles were not considered here since it was our purpose to determine
whether a PUDVM system with given operating characteristics could
adequately describe the nature of the various velocity profiles.
Velocity information from the PUDVM is contained in a frequency
modulated audio signal that is obtained by mixing the backscattered
(or Doppler shifted) ultrasound signal with an ultrasound signal at
the transmitted frequency. The frequency difference between these
two signals, the Doppler frequency, is directly proportional to the
velocity of the moving scatterers in the sample region and is given
by the Doppler equation
2f V cos 0
Af = f D = ^ir — 0)
where f is the frequency of the emitted ultrasound, V the velocity of
the scatterers, e the angle between the ultrasound beam and the velocity
vector and C the speed of sound in the medium. Since the PUDVM sample
region is of finite size, a spectrum of Doppler frequencies will be
measured in any flow field where velocity gradients exist such as in
a contained flow.
The purpose of the experiments reported here was to compare different
methods of determining the average frequency shift of the Doppler spectrum
-42-
o r, equivalently, the average speed of the moving scatterers within the
region of flow sampled by the PUDVM. Three techniques were used
to estimate the average frequency of the Doppler signal: (1) direct
frequency to voltage conversion using a zero crossing detector; .
(2) calculation of the first moment of the Doppler spectrum obtained
with the aid of a spectrum analyzer; and (3) computer-aided estimation
of the first moment of the Doppler spectrum using Fast Fourier Transform
(FFT) techniques. Average velocities in the sample volume were calculated
from the average frequencies using the Doppler equation and the resulting
profiles were compared to the theoretically predicted velocity distributions.
B. Methods
The experiments were conducted in a specially designed test system
which is shown schematically in Figure 14. The flow system produces
steady fully developed laminar or turbulent flow in dialysis tubes
ranging in size from 6 to 20 mm diameter. The test section consists
of a long length of circular dialysis tubing supported and submerged
in a water bath. Measurements were made at positions located several
hundred tube diameters downstream from the entrance to the dialysis
tubing to ensure that the flow was fully developed'. Flowrates were
monitored with a rotometer and could be adjusted with an inlet valve.
The performance of the rotometer was verified by turned collection
and found to be accurate to within 5% of the manufacturer's calibration
values. The working fluid in the test system was water seeded with
cornstarch or cellulose particles to act as scatterers of the ultrasound.
/ '
Concentration of the scatterers was typically 5% by volumev.
An ultrasound transducer was positioned over the dialysis tube
in the vertical plane determined by the tube axis and with the ultrasound
-43-
beam axis at an angle of 60° to the direction of flow. The transducer
consisted of a 2.8 mm diameter lead titanate zirconate crystal with
epoxy backing.
Velocity and frequency data were obtained with the PUDVM for
flow Reynolds numbers ranging from 950 to 5000. All measurements
reported here were monitored in the flow system in a dialysis tube of
nominal diameter 7 mm. The tube diameter varied with flow rate from
7.2 to 7.6 iron and this variation was considered in the calculation
of the Reynolds numbers. For these tests, the PUDVM emission frequency
ranged from 7.25 MHz to 7.5 MHz. Other operating parameters included
an emission pulse length of 8 cycles (about 1 psec) gate of 1 ysec
and pulse repetition frequency of about 20 KHz.
For each Reynolds number the velocity profile as measured from the
output of the zero-crossing detector was recorded on graph paper using
an X-Y plotter. The RMS voltage of the audio signal was monitored with
a B and K RMS voltmeter. Peak RMS audio amplitude was maintained between
0.15 and 0.25 volts RMS and the signal to noise ratio of the audio
signal was at least 40 volts/volt. The velocity signals were scanned
continuously across the tube for each Reynolds number. A spectrum
analyzer (Hewlett-Packard model 8552/56) was used to determine the
frequency spectra of audio signals measured at several range locations in
the tube. The relative amplitudes of the frequencies present in the
signal were recorded as a function of frequency on the X-Y plotter.
The recorded spectra were subsequently used to determine the first
moment of the Doppler signal. In addition, audio signals from these
same range locations were recorded on magnetic tape for computer
analysis using FFT techniques.
-44-
C. Results
Typical recordings of a velocity profile and frequency spectra
for laminar flow (Re=T430 ) are shown in Figures 15 and 16. A tracing
of the continuous velocity profile is plotted in Figure 15 as a
function of the distance from the centerline of the tube. The measured
profile is shown here compared to the theoretically predicted profile.
The measured profile is spread at the far wall and the obvious hump
on the velocity profile between the near wall and the center of the
tube is apparently due to the PUDVM boundary error (1). In this
example, the PUDVM underestimates velocities close to the near wall
and overestimates velocities at the far wall. The measured centerline
velocity is within 3 % of the predicted value.
The frequency spectra at six locations in the tube are shown in
Figure 15. The spectra were measured at range increments of 1 psec
across the tube however for clarity the data presented in Figure 3
are for increments of 2 ysec. For each spectrum the baseline was
set approximately 8-10 db below the peak signal level. The baseline
levels (in db) are referenced to a sinusoidal input signal of 1.0 V
RMS. The noise baseline for zero flow was -70 db or less. The first
moment of the Doppler spectrum was determined from these data and the
average velocity within the sample region calculated using the Doppler
equation.
A comparison of the theoretical velocity profile, the measured
profile (using analog output of PUDVM) and the profile calculated from
the first moment of the Doppler spectra are shown in Figure 17. The
solid line is the predicted profile, dashed line the measured profile
and the points correspond to the calculated profile. Agreement between
the predicted profile and either the measured or calculated profile is
- 45 “
excellent within the central core of the flow and the measured and
calculated distributions are within 10% of each other except near the
walls of the tube. For distances from the wall less than 1/4 the
tube radius both the zero-crossing counter and first moment calculation
lead to substantial errors in the velocity estimate for this example.
Similar comparisons can be made for the case of fully developed
turbulent flow. Figures 18 and 19 illustrate the measured velocity
profile and Doppler frequency spectra respectively for a flow with
Reynolds number 3860. The measured profile is compared to the
theoretically predicted mean velocity distribution given by Schlichting
(2) as
= k£) 1/n
u K
where u * axial velcoity, u" = average axial velocity, and n and k
depend upon the Reynolds number. For Reynolds numbers from 2000 to
5000 k and n remain approximately constant and have values of .791
and 6.0 respectively.
Over the central 80% of the tube cross section the PUDVM consistantly
overestimates the mean velocity by 5 to 10%. The shape of the measured
profile is again somewhat smoothed and especially distorted near the
tube walls.
The Doppler frequency spectra for this example of turbulent flow
are shown in Figure 19. They are considerably more broad than the spectra
observed in laminar flow because of the random distribution of turbulent
velocity fluctuations that are superimposed on the mean flow. The
spectra remain relatively symmetric however. Figure 20 shows the profile
calculated from the first moment of the Doppler frequency spectra along
-46-
wlth the measured and theoretical profiles. The profile based on the
first moment agrees well with the measured profile except in the
neighborhood of the walls.
Comparisons among measured, calculated and theoretical profiles
for seven different Reynolds numbers are summarized in Figures 21-
27. Theoretical profiles are shown in solid line, measured in dashed,
and the dots represent velocities calculated from frequency spectra.
Computer aided estimates of the velocity profiles were obtained
using Fast Fourier Transform (FFT) techniques to calculate the first
moment of the Doppler spectra. Operation of the FFT program used for
this analysis is described in Appendix I. Typical results of the FFT
analysis are shown in Figures 28-34. The FFT estimated profiles are
compared to theoretical profiles for Reynolds numbers ranging from
950 to 4800. The FFT consistantly overestimates velocities for both
laminar and turbulent profiles. For laminar flow the estimated
profiles have the characteristic parabolic shape of the velocity
distribution in a circular pipe, however, the peak (centerline)
velocities are overestimated by 15 to 20%. The shapes of the calcu-
lated turbulent profiles are not in obvious agreement with theoretical
predictions.
D. Observations
1. In laminar flow, the velocities in the central core of the
tube (+0.6 radius from the tube center) as measured by the zero-crosser
and first moments from the wave analyzer spectra agree within 5% with
the expected theoretical velocities.
2. In turbulent flow, estimates of velocities within the central
core of the tube by the zero-crosser and first moment from the wave
-47-
analyzer agree with each other within 2-3%, but both peak velocity
estimates are 6-17% higher than the expected theoretical velocities,
the error decreasing with increasing Reynolds number. This over-
estimation of velocities was consistently found in repeated experiments.
3. Velocities estimated from the audio spectra using FFT and
computer techniques are from 10% (in laminar flow) to 22% (in turbulent
flow) higher than the expected theoretical values.
4. In flow near the walls, the velocities estimated by spectral
analysis, both with the wave analyzer and FFT, are many times the
expected theoretical values. This is most likely due to the low power
of the signals near the wall. In the case of the wave analyzer,
spectra obtained near the wall often had a baseline level only 10 db
above the noise level. Inclusion of white noise into the spectra would
tend to shift the first moment of the spectra toward higher velocities.
5. Overall, the zero crossing counter provides a velocity estimate
that is at least as good as the velocity calculated from the first
moment of the Doppler spectrum. Near the walls, the zero cross er
gives a better indication of the true velocity than the frequency
spectrum.
E. Conclusions
1. Central core velocities as estimated by the zero crosser and
the first moment from the wave analyzer spectra agree well with
each other, but are only estimates of the true velocity in laminar
flow.
2. The velocities estimated by the first moment of the FFT
analyzed audio signal are not accurate estimates of the true velocity.
3. Since the zero crosser is more reliable near the walls, it
- 48 -
gives a more accurate estimation of the velocity profiles than does
the first moment of the audio spectra from the wave analyzer. However,
since the baseline level of the audio signal near the wall was not held
constant and, in fact, often approached noise levels, an electronic
first moment processor might prove as accurate as the zero crosser
near the walls.
Constant Head Tank
Figure 14 Schematic Drawing of Test Tank Used to Produce
Fully Developed Laminar and Turbulent Pipe Flow
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- 64 -
IX. Performance of the NASA-PUDVM
A. Objectives and Methods
The PUDVM designed and built by the NASA Ames Research Center
was loaned to our laboratory for use in animal experiments and for
testing and comparison with other pulsed Doppler velocity meters.
The NASA instrument was used for studies on coronary blood flow in
horses and the pertinent physiological and biomechanical results
have been summarized in the report "Hemodynamic Patterns in Coronary
Arteries" by Wells et. al. This report is included here as Appendix
II.
The performance of the PUDVM was determined from tests carried out
on the flow system described above in Section V. In general the performance
of the NASA- PUDVM in the tank facility was inferior to the performance
of the McLeod instrument. This was attributed to the low signal to noise
ratio and the low sensitivity of the NASA-PUDVM. It was decided that
any detailed evaluation of the PUDVM capabilities and subsequent
definition of techniques for the transcutaneous measurement of flow
should be based on tests with the McLeod PUDVM. These results are
described above in Section V.
The effect of emission pulse length, gate length and pulse repetition
frequency on the performance of the NASA-PUDVM was determined by
comparing the velocity profiles measured for steady laminar flow in
the test system. In addition, the accuracy of the flowmeter was
measured for different input gains.
B. Results
An important factor that strongly affects the accuracy of the
PUDVM is the signal to noise ratio S/N. The number of scatterers
-65-
directly influences the strength of the backscattered Doppler signal
and it was found that in tank studies with the NASA-PUDVM the test
fluid had to contain a 10 to 15% concentration of scatterers to bring
the signal to an acceptable level. However, with a high concentration
of scatterers a proportionally larger number of particles would settle
to the bottom of the tube and distort the profile from the desired
parabolic shape. It was not found practical to run the test system
for more than a minute or two with particle concentrations greater
than about 10% by volume. Even at this concentration, however, the
two input amplifiers had to be operating at their maximum effective gain
in order for the PUDVM to properly estimate velocity. To determine
the sensitivity of the PUDVM to input gain, the following experiment was
performed: The PUDVM sample region was centered on the tube axis
and flow maintained at a constant rate. The output of the PUDVM
was measured for various settings of the "gain 11 and "range" amplifiers
and compared to the expected output which was determined from the
calibration signal. The results are given in Figure 35 which, shows curves
of output vs. gain for five values of range gain. Notice that only
for range gains of 95 and 100% of full scale was the PUDVM output within
5% of the expected value. Furthermore -in order to achieve this adequate
output the gain was in excess of 70% of its full scale value. For gains
above about 75% the audio signal became distorted and the output would
decrease slightly. Hence to measure velocities accurately in the tank
system the range gain had to be set between 95 and 100% and the gain
between 70 and 75%. The optimum operating point was easily found
by maximizing the output of the PUDVM with the two gain controls.
However, there was not guarantee that the maximum output would agree
*
with the expected output. This difficulty was particularly acute
- 66 -
when attempting to use the PUDVM to measure velocities at distances
more than a few millimeters from the transducer. For this reason,
the NASA-PUDVM is not suited for transcutaneous measurements of
hemodynamic patterns. On the other hand, when measuring blood flow
in animals with transducers positioned directly on the vessel, the NASA-
PUDVM estimates the time varying velocity as well as the McLeod
PUDVM. This fact was confirmed by direct comparison of the NASA
flowmeter with the McLeod detector. It appears that when the ultrasound
pulse is scattered from cells in whole blood (45% concentration
of scatterers) the power in the received echo is sufficient to produce
an acceptable signal to noise ratio within the PUDVM. The output of
the zero Grosser then provides an accurate measure of the velocity.
The NASA-PUDVM operates with an emission pulse of 4, 8, or 16
cycles and at a pulse repetition frequency of 13, 26, or 52 KHz,
To obtain sufficient S/N ratios in the tank studies the PUDVM generally
had to be operated with the maximum burst length and at 26 or 52 KHz
PRF.
Velcoity profiles within the dialysis tubing were obtained by
slowly scanning the PUDVM sample volume across the tube and plotting
the velocity estimate as a function of delay time (range). Figure 36
illustrates two measured profiles and compares them to the predicted
parabolic profile. The measurements were made with an emitted pulse
of 16 cycles, a gate of 1 ysec and at PRFs of 26 and 52 KHz. The shapes
of the measured profiles agree well with the true profile and there is
no significant effect of PRF on the estimated profile. The measured
centerline velocity differs by less than 5% from the predicted value and
this difference is well within the anticipated experimental error.
-67-
The distortion of the measured profiles at the near wall appears to
be less than near wall distortion observed in the flow system using
other pulsed Dopplers. This might be due to the low sensitivity
of the NASA-PUDVM, for if the detector is sampling only the peak of
the Doppler spectrum, the effective sample region would be reduced.
In addition, the power of the received signal would be diminished
leading to an underestimation of the true velocity. This effect is
evident in Figure 36. The fact that increasing the sample gate from
1 ysec to 5 ysec does not markedly affect the measured profile and lends
some support to this interpretation.
Figure 37 shows the effect of sample gate on the measured profile.
Again distortion or spreading of the measured profile is not apparent
at the near wall. As the sample gate is increased, the profile is
spread, however, not to the degree that one would expect if the effective
sample region increased at the same rate. That is, increasing the gate
tends to increase the power in the received signal more than it tends
to distort the profile. The increase in signal power leads to an improved
estimate in velocity. Between the near wall and centerline of the tube,
the velocities measured using a 5 usee gate are in excellent agreement
with the true values.
Figure 38 shows the effect of burst length on profiles measured
with the NASA-PUDVM. The power of the backscattered signal varies
as the length of the emitted pulse. Since this detector is extremely
sensitive to signal strength, we expect inferior performance when using
shorter pulse emission times. . This prediction is borne out by the
curves in Figure 38, especially for emitted bursts of 4 cycles.
The same response is expected for decreased pulse repetition frequencies.
- 68 -
Figure 39 illustrates the effect of halving the PRF when using an emitted
pulse of 8 cycles. For a PRF of 25 kHz the measured peak velocity is
more than 20 % in error.
C. Discussion and Recommendations '
It was not possible to fully evaluate or calibrate the NASA-PUDVM
under the test conditions described above. The major problems were
the low gain of the detector and the low S/N ratio. Backscattered
power could be increased by using more or larger scatterers or scatterers *
having a greater scattering cross-section. However, additional problems
such as particle settling, profile distortion and non-specular scattering
are encountered. The NASA-PUDVM appears to operate satisfactorily
when measuring in blood, however it was not practical to use blood in
the test system. Improved signal amplification techniques should
markedly improve the performance of the NASA-PUDVM and allow for a
more extensive evaluation of the instrument.
The following suggestions are made to improve the utility of the
NASA-PUDVM. To optimize the instrument performance for use with different
transducer material and transducer configurations, provision should be
made for easily adjusting the emission frequency. At present, in order
to change the ultrasound frequency it is necessary to tune both the
master oscillator and the receiver amplifier circuit. These adjustments
are inconvenient to make and time consuming. When using the flowmeter
for measurements in animals, it is virtually impossible to readjust
the PUDVM as different transducers are used. Operating an ultrasound
transducer at a non resonant frequency markedly reduces its sensitivity.
Calibration of the NASA-PUDVM could be simplified if the calibration
signal was a frequency of a fixed percentage of the oscillator frequency.
- 69 -
As designed* the device provides a calibration voltage proportional to
a specific Doppler frequency shift. To calculate the corresponding
velocity it is necessary to know both the speed of sound in the test
fluid and the PUDVM center frequency. By using a known percentage of
the center frequency, only the speed of sound- would have to be known
to determine the calibration velocity.
70
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Fiftuar 39
-75-
X. Standard Test System
A. Objective
The objective of this work was to develop and test a hydraulic
flow system that could generate a uniform laminar flow with a linear
velocity profile and constant velocity gradient. This system could
be used as a standard for evaluating and calibrating pulsed ultrasound
flowmeters and transducers- The system was also to be used to determine
the characteristics of the sample region. When sampling a linear velocity
profile the spectrum of the Doppler audio signal provides a measure
of the true spatial distribution of the sample region. In this case,
the Doppler frequency is proportional to range and length of the sample
region is obtained directly from the band width of the audio spectrum.
B. Design
An almost linear velocity distribtuion can be generated between
two concentric cylinders by rotating the outer cylinder at a constant
rate and holding the inner cylinder stationary. For this case, the
velocity as a function or radius r is given by
v(r) =
u.0+7-) 2
r i
f(2+r)
M r l
(r- -H
where r^ is the radius of the inner cylinder, h the distance between
cylinders and w is the angular velocity of the outer cylinder. Referring
to Figure 40; for a transducer location at r=r-| having a beam inclined
at an angle a to a radius vector passing through the transducer, the
velocity component along the beam at radius r is V(r)cose=V^ where
cos6=(r.| sina)/r. This is the component of velocity that the PUDVM
will sense and the corresponding Doppler frequency is
-76-
2foV.
Af =
Radial position r is related to the distance along the beam R and
can be determined from the law of cosines. The Doppler velocity
then becomes
V D =
wr-jSina
1-
1
o
1
h \2
0'*r L )
r 1
!+(#-) 2 + 2(~)cosa
r i ^
]
In order to sense a linear velocity distribution, the Doppler velocity
should vary directly as range R. The degree to which V D approximates
a linear function depends on a and the ratio R/r-j. The parameters
r-j , h/r^ and w only effect the magnitude of V^. Defining the function
g(TT-.a) as
r 1
gfcr-. a) = [1
r l
1
1 + (#-) 2 + 2(^)cosa
r l M
■]
the normalized velocity distribution as a function of normalized range
is given by plotting g(-— , a) vs. R/r, for various values of a. This
1 R
relationship is depicted graphically in Figure 41. Notice that for — >
0.1 deviations from linearity depend strongly on a. The normalized
velocity closely approximates a linear distribution for values
of a about 70°. The deviation from linearity can be determined by
comparing the actual velocity at any range with the corresponding
velocity based on a linear distribution where the linear and true
profiles have the same peak velocities. In general, the maximum
difference between these two velocities is less than 5% of the peak
velocity for 60°<a<80°. Hence, to a good approximation, the measured
velocity profile will appear linear. The above derivation and conclusions
do not account for finite width of the transducer beam and the errors
-77-
tha t may arise. At a given distance from the transducer, a cross
section of the beam will sense a band of velocities with an average
equal to the value at the center. Although this effect is not expected
to introduce significant errors in the velocity estimate, it will
cause a frequency spreading in the audio signal. This spreading is
minimized for large values of h/r-j and for samples taken at large R and
does not depend strongly on a. For h/r-j > .25 the bandwidth of a sample
region of zero length will be less than 5% of the peak Doppler frequency
for a transducer with radius .01 r-j.
A schematic of the flow system is shown in Figure 42. The cylinders
are made of 1/2" thick aluminum and the outer cylinder is mounted
on a turntable which is supported by a thrust bearing. The inner
cylinder is stationary and suspended within the outer cylinder by two
supports. The turntable is connected to a variable speed dc motor with
a rubber belt. A transducer and transducer holder are shown in Figure
43, which also indicates how the transducer is positioned in the flow
system. The ultrasound beam lies in a horizontal plane.
C. Results
Only preliminary measurements of velocity profiles and sample
volumes have been made using the standard flow system. A detailed
summary of the effectiveness of this system for calibrating flowmeters
and determining transducer characteristics will be included in the next
semiannual report on this project. The working fluid was a water-
glycerol solution of viscosity .04 dynes- sec/ cm 2 seeded with cellulose
particles. The Reynolds number based on the gap width and average
velocity in the gap was less than 2000 thereby assuring laminar flow. A
velocity profile across part of the gap is shown in Figure 44. The
-78-
PUDVM was operated with a burst of 8 cycles (f =7.04 MHz) and a gate
of 1 ysec. The zero offset on the range axis results from the fact
that the ultrasound crystal is recessed about 3 mm from the edge of
the inner cylinder. The range is given in mm from the edge of the
cylinder. The profile is linear for R < 10 mm but deviates significantly
from linear for R > 10 mm. The transducer used for this test had a
diameter of about 1.9 mm and the power of the backscattered signal
dropped rapidly for R > 10 mm. This could account for the deviation
in the profile. Additonal tests will be conducted using blood in the
flow system which should give a stronger signal and improved S/N ratio
at large R.
To estimate the length of the sample region, the window or receiver
gate was positioned within the linear portion/ of the profile and the
frequency spectrum of the audio signal was measured. Since the frequency
of the backscattered signal increases linearly with distance from the
transducer, the frequency spectrum of the return signal, i.e. the power
spectrum of the Doppler signal as a function of frequency, is equivalent
to the power of the signal as a function of range. Hence, the plot
of the frequency spectrum gives the shape of the sample region along the
beam axis. Figure 45 gives frequency spectra of the Doppler signal for
various sample gate lengths. Only about 10 db of the audio power spectra
are shown. For a gate of 1 ysec the bandwidth of the spectrum is about
725 Hz which corresponds to a sample length of about 3 mm along the
beam. As the sample gate is increased from .5 ysec to 4 ysec the bandwidth
of the sample region increases ffom about 700 to 900 Hz. This corres-
ponds to an increase in the length of the sample region of less than .3 mm
for each 1 ysec increase in gate time. This estimate of sample length
-79-
only includes that portion of the sample region where the power of
the Doppler signal is more than about 10% of the peak power of the
return signal. The extent to which the effective sample region is
broadened by the low power Doppler signals must still be determined.
Additional studies will be made using this linear profile
flow system to test the effects of transducer material and backing, gate
width, burst length and delay on the length of the sample region.
K»* 5
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BIBLIOGRAPHY
1. Interim Report, "Transcutaneous Measurement of Volume Blood Flows,"
prepared for NASA-Ames Research Center under NASA Grant NSG-7009,
August 1 , 1974.
2. Schlichting, H., "Boundary Layer Theory," McGraw-Hill, 1968.
-87-
Appendix I
FFT PROGRAM TO ANALYZE ULTRASONIC PULSED DOPPLER AUDIO OUTPUT
The purpose of the program is to perform a frequency analysis on the
Doppler shifted audio signal and to thereby provide values indicating
the variation of blood velocity with time.
The audio signal is divided into short time intervals and each
interval is analyzed using a discrete Fourier transform, the transform
is then used to calculate the power spectrum for the interval, i.e. the
amount of power inthe signal at each frequency. A method is then used
to select the frequency "most representative" of the interval and from
this frequency a velocity can be caluclated using the relation:
V = ^
2fo COS a
where c represents speed of sound in blood, fo is the ultrasound
frequency emitted, a is the angle between the ultrasound source and
the direction of blood flow, Af is the Doppler frequency and V
is the velocity. Once the velocity has been obtained for each interval,
the time varying velocity can be constructed for a 1 second interval.
Program Structure
Input to the program consists of digital data on tape obtained by
digitizing the pulsed Doppler audio signal. At present the analog
signal is digitized using a sample rate of 25.6 kHz. This will
provide sufficient information to Fourier transform a signal up to
12.8 kHz, much greater than the expected Doppler shift.
The input physical record is 256 words long, each word containing data
values in packed format. Thus, each physical record represents 1280
data points.
- 88 -
Program output is a series of microfilm plots of power spectra for
each interval analyzed and time varying velocities for each second
of time. 1
Analysis
The audio signal is treated in lengths of one. second, and at present
is divided into intervals in 1 /100th second. The frequency resolution
of the Fourier analysis increases with the length of time interval,
thus long intervals are desirable. However, with long intervals, time
resolution suffers and information about a rapidly varying signal will
be lost so that for this consideration short time intervals are preferable.
A method is used which attempts to combine these approaches, in the hope
of gaining the advantage of both.
The data invervals of 1/1 00th second are analyzed in pairs, equivalent
to a time interval of 1 /50th of a second. Subsequent pairs are formed
from the last member of the preceding pair and the data interval
following it. Thus a frequency resolution of 50 Hz is obtained and
the analysis is performed every 1/1 00th of a second and time resolution
is preserved. Each 1 /50th of a second interval is transformed using
the fast Fourier transform, the square of the transform gives the power
at each frequency.
The problem now is to select the frequency considered to best represent
the power spectrum. The method used is to calculate an average frequency
according to the formula:
_ 1 pifi where Pi is the power
f = and fj -j s frequency
z Pi
In order to limit the effect of noise on this computation, it is repeated,
using only the portion of the. spectrum lying within ± 1.25 kHz. This
is in effect a filter or data window.
- 89 -
Its effect is to "stretch" the resulting frequencies along the y
axis such that peak velocities are high and low velocities near
zero.
At present three velocity plots are made using frequency of peak
power for each interval, average power and average filtered power.
In addition, there is a printout giving the actual value of the
frequency for each interval using these three methods.
-90-
APPENDIX II
HEMODYNAMIC PATTERNS IN CORONARY ARTERIES
by
M. K. Wells*
D. C. Winter**
T. C.' McCarthy'*'
A. W. Nelson
ABSTRACT
A pulsed ultrasound Doppler velocity meter has been used to map
the time varying velocity waveforms in the exposed left coronary arter-
ies of anesthetized ponies. Velocity measurements were made without
invading the vessels or disturbing the hemodynamic patterns. Typical
recordings of velocity waveforms and calculated velocity profiles In
the main, descending and circumflex branches are presented. Marked local
velocity fluctuations were measured in the major coronary branches and
appear to result from longitudinal vibrations of the vessels. In general
the coronary flows are characterized by peak Reynolds numbers of 300 to
600 and maximum shear rates of 400 to 600 sec
* Assistant Professor, Department of Mechanical Engineering.
** Graduate Research Assistant, Department of Mechanical Engineering,
t Graduate Research Assistant, Department of Clinical Sciences,
tt Associate Professor, Department of Clinical Sciences.
Colorado State University
Fort Collins, Colorado 80523
- 91 -
HEMODYNAMIC PATTERNS IN CORONARY ARTERIES
INTRODUCTION
The hydrodynamic events of blood flow appear to have a strong influence
on the development and distribution of arterial disease. Fry [1]* and Caro
et al . [2] have suggested relationships between arterial wall shear stress
and the development of atherosclerosis although the exact role of the shear-
ing stress in the disease process (i.e., whether it is a causative or con-
trolling factor in atherogenesis) has not been resolved. The frequent
involvement of the left coronary artery and its branches in atherosclerosis
necessitates a complete description of the normal hemodynamic patterns in
these vessels in order to understand the role of fluid mechanics In athero-
genesis. In particular, local blood velocity gradients, especially near
/
the vessel walls, may be most significant in governing the disease process.
Indeed, the behavior of the flow near the wall markedly affects the trans-
port of substances across the endothelium and determines the nature of the
flow Induced mechanical stresses on the vesselwall.
In general, arterial blood flow can be described as nonsteady and
laminar although flow disturbances and turbulence might be expected to
occur near the entrance to the aorta and in vessels having complex geometry.
In addition, blood flow is not necessarily unidirectional. Because of the
pulsatile nature of the heart (pump) and the di stensibility of the vessels,
flow reversal is typically observed in large arteries and may often be
accompanied by periods of three dimensional flow. Secondary flows can be
generated by centrifugal effects and would be expected in the arch of' the
♦Numbers in brackets designate References at end of paper.
-92-
aorta or near arterial branches. Similarity parameters of interest for
studies of arterial hemodynamics are the Reynolds number Re - UD/v based
on either the peak or the average forward velocity and the Womersley [3]
unsteadiness or frequency parameter a = R(uj/v) Js (U = velocity, D ■* 2R =
vessel di ameterv v-" -kinematic- viscosity -and u> frequency of the flow,. ... ■
oscillations). Since the flow is not purely sinusoidal, a represents the
ratio of the vessel radius to the thickness of the oscillation boundary
layer associated with each harmonic component of the blood flow pulse.
Alternatively, taking m equal to the heart rate or fundamental frequency
of the flow oscillations, a 2 can be interpreted as the ratio of the time
required for a velocity change to be transported across a vessel by viscous
transport to the time of one cardiac cycle. In animals these parameters
may vary rapidly and over a wide range depending upon such factors as the
physiological condition of the animal or the consequences of surgical pre-
parations. In general, the maximum Reynolds number is less than 10,000
and the unsteadiness parameter less than 25.
Although abundant information is available regarding the fluctuations
and distribution of volumetric flows in the cardiovascular system, .'our
understanding of the fluid mechanics of the circulation requires a descrip-
tion of the velocity distribution patterns and local velocity waveforms
throughout the arterial system. At present, only two methods have been
successfully applied for “point" velocity measurements in the arteries of
living animals: hot-film anemometry [4-7] and pulsed ultrasound Doppler
techniques [8-10]. To measure blood velocity with an anemometer system a
hot-film probe is placed directly into the flow stream either by vessel
- 93 -
puncture or with the aid of a catheter. Velocity profiles are constructed
from time varying velocity waveforms obtained at various locations in the
lumen cross section as the probe is traversed across a- vessel diameter.
When the hot-film probe is positioned near the vessel wall, the normal
flow pattern in that region is altered and the corresponding velocity wave-
forms do not represent those of the undistrubed system.
The pulsed ultrasound Doppler velocity meter (PUDVM) provides a less
traumatic measurement of blood velocity than a hot-film anemometer since
it is possible to monitor velocity waveforms extraluminally or transcutan-
eously. The PUDVM operates in a radar-like mode which allows measurements
to be made at specified ranges within a blood vessel. This differs from
continuous wave (CW) ultrasonic velocity detectors which lack range resolu-
tion and are used to measure volumetric flow rates. The PUDVM measures the
average velocity of blood cells in a small volume within a blood vessel by
sensing the change in frequency of ultrasound scattered by the moving
particles. Velocity waves from sample volumes located at Increments across
the vessel lumen are obtained by electronic range gating and velocity pro-
files at speclfid instants of the cardiac cycle can then be constructed.
In addition to the fact that this measurement technique is noninvasive in
the sense that the blood vessel walls remain intact, it has the additional
advantage of not disrupting the normal blood velocity patterns. The pulsed
ultrasound flowmeter is suited for measuring velocity distributions in
arteries as small as 6 or 7 mm in diameter and has been employed in moni
toring blood velocity waveforms in the canine carotid and femoral arteries
DO].
“94-
METHODS
Pulsed Ultrasound Velocity Meter
The transducers used in this study consist of a small disk of lead
titanate zirconate (PZT-5) bonded with epoxy to the inner surface of a
polystyrene holder which is fashioned in the form of a half cuff. The
circular piezoelectric disk acts as both the emitter and receiver of ultra-
sound and is mounted such that when the half cuff rests on the surface of
a blood vessel the crystal is positioned at an oblique angle to the flow.
The cuffs range in size from 3 to 7 mm diameter and contain crystals of
1.5 to 2.5 mm diameter.
The pulsed Doppler velocity detector used In these studies was developed
by the NASA Ames Research Center and Is based on a design by F. D. McLeod.
The directional PUDVM generates pulses of 7-8 MHz ultrasound 4, 8, or 16
cycles in length and at a repetition rate of 13, 26, or 52 kHz. These
pulses are used to drive the transducer which directs acoustic waves into
the tissue structure and blood vessels. Echoes from these structures and
from blood cells are received by the transducer during the interval between
pulses. The arrival of the backscattered ultrasound at the transducer is
delayed in time by an amount proportional to the distance between the trans-
ducer and the scatterer and the frequency of the returning ultrasound Is
shifted in proportion to the velocity of the blood cells which traverse
the ultrasound beam. The velocities of the moving targets are calculated
directly from the Doppler formula:
V =
Af C
2 f cose
(D
where V is the target or particle velocity, Af the Doppler frequency shift
-95-
of the backscattered ultrasound, f the frequency of the emitted ultra-
sound, c the speed of sound in blood or tissue and 0 is the angle between
the ultrasound beam and the target velocity vector. By time or range
gating the return signal, echoes from targets within specific regions of
the vessel can be selected for processing. The size qf the sample region
is determined primarily by the characteristics of the transmitted ultra-
sound pulse, the transducer radiation pattern, the time over which the re-
turn signal is observed and the sensitivity of the signal processor. For
the PUDVM and transducers used in these experiments the effective sample
region was determined to be about 1 to 1.5 mm in depth while the cross
sectional area of the sample region is approximately equal to that of the
piezoelectric crystal [11].
The frequency of the backscattered signal received by the transducer
during the observation period is compared to the frequency of the original
emitted burst in order to d^ter^ine the Doppler shift or difference fre-
quency Af. An analog voltage proportional to the Doppler frequency is
obtained with the aid of a zero crossing detector and serves as a measure
of the average velocity of the scatterers within the sample volume. Pro-
cessing the signal in this fashion limits the output frequency response
of the PUDVM to about 15 Hz, however, the instrument is equally sensitive
to velocities in the forward and reverse directions.
Velocity Measurements in Coronary Arteries
A pulsed Doppler velocity meter was used to monitor blood velocity
waveforms in the left coronary arteries of 12 ponies of unknown age and
history. The ponies ranged in weight from about 125 to 250 kg. Anesthesia
-96-
was induced and maintained by an intravenous administration of barbltuate
and positive pressure ventilation was provided throughout the procedure.
The animals were placed in right lateral recumbancy and the chest was
entered through a routine left fourth intercostal thoracotomy incision.
The lungs were retracted from the operating field and the pericardium opened
with a T-shaped incision. The epicardial fat pad was opened immediately
over the majo** branches of the left coronary artery which lie in the coro-
nary groove on the surface of the heart. The main branch of the left
coronary artery is short and divides within a few millimeters of its origin
at the root of the aorta into an anterior descending branch (LAD) and a
circumflex branch. At the bifurcation the LAD branch generally proceeds in
a straight line from the main branch whereas the circumflex branch joins at
an angle of about 90 degrees. Segments of the left common coronary artery,
circumflex branch and descending branch were isolated from the surrounding
tissue over lengths of 1 to 2 cm to allow for positioning of the flow trans-
ducers. Measurement sites were 1 pc a ted on the main, circumflex and descend-
ing branches immediately adjacent to their common junction and on the
descending branch 2 to 5 cm below the coronary bifurcation. A half cuff
\
was placed on the vessel at the chosen site and secured to the vessel with
a strip of umbilical tape 5 rren in width. Care was taken not to distort or
partially occlude the vessel in order that the normal hemodynamic patterns
would be maintained. Acoustic coupling between the ultrasound transducer
and the blood vessel was provided by Aqua sonic gel or a small blood clot
placed between the piezoelectric crystal and the vessel wall. Time vary-
ing velocity waveforms were measured at increments of .5 to .75 mm along
-97-
the path of the ultrasound beam between the near and far walls of the vessel.
The beam was inclined at an angle of 45 to 60 degrees to the longitudinal
axis of the artery and the direction of the velocity vector was assumed to
be parallel to this axis. Eight to twelve sequential velocity waveforms
were obtained at each range location and a single scan across the vessel
would require from 2 to 4 minutes to complete. Velocity data and an electro-
cardiogram were recorded on a strip chart and on magnetic tape for subse-
quent computer processing and analysis.
RESULTS
Figure 1 is a computer plot of one cycle of an average centerline
velocity waveform obtained in the LAD branch and illustrates the general
characteristics of a coronary flow or velocity pulse. The beginning of
the cycle coincides with the R-wave of the electrocardiogram which signifies
the onset of ventricular contraction. During the first part of the cardiac
cycle (systole) intramusc'jl^ pressure t.h« contracting left ventricular
t
wall increases and causes the peripheral coronary arteries, capillaries
and veins to close leading to a marked decrease or transient cessation of
left coronary artery flow. As the heart muscle relaxes and the hydraulic
impedance of the coronary circuit decreases the blood velocity Increases
rapidly and the maximum flow generally occurs during the latter portion of
the heart cycle (diastole). This behavior is evident in the record of
Figure 1 which shows the-LAD velocity decreasing during systole from an
initial value of 115 cm/sec to about 20 cm/sec and then rising again to
about 120 cm/sec during diastole. Based on a vessel diameter at peak for-
ward flow of 5 inn the maximum Reynolds number for this example is 1500 and
-98-
the Womersley unsteadiness parameter for the heart frequency is about 3.5.
Velocity and flow oscillations in the frequency range* of 5 to 10 Hz
are often measured during systole and early diastole. It appears that the
ventricular contractions generate stress waves that propagate through the
heart muscle (myocardium) and cause the coronary arteries to vibrate.
These waves are readily observable as they travel across the surface of
the heart and their intensities can vary markedly. The presence of this
type of wave is seen on the velocity record in Figure 1 and appears to in-
duce an oscillation at about 7 Hz on the mean coronary velocity during late
systole. The low amplitude high frequency fluctuations seen on this veloc-
ity record (particularly evident during late diastole) are due to statisti-
cal variations in the output of the zero crossing detector which is used
to convert the Doppler frequency shift to an analog voltage. The fluctua-
tions do not represent flow disturbances or turbulance.
Estimates of the time varying velocity profiles in this same vessel
are constructed using the average velocity waveform for each range location
and are shown in Figure 2. Profiles are calculated at 18 equally spaced
time intervals during the heart cycle and are plotted sequentially with a
10 cm/sec offset between each profile for the sake of clarity. Figured
(a) begins at the bottom with the profile for t=o and ends at the top with
the profile in the cycle having the greatest average forward velocity.
\
Remaining profiles are given sequentially in Figure 2 (b) beginning with
the uppermost curve. The last profile of the heart cycle is at the bottom
of Figure 2 (b). In the profile calculations account is made for the trans-
ducer orientation and the profiles are plotted as a function of distance
d * « %
-99-
from the transducer along a line normal to the vessel axis. The diameter
of the flow stream can be estimated from the width of a velocity profile,
however, significant errors may be introduced since the profiles are dis-
torted near the walls due to the finite sample volume of the PUDVM. In
order to compare relative vessel size among the animals studied, vessel
diameters were estimated from the peak forward velocity profile. The dis-
tance between the intersections with the zero velocity axis of the lines
tangent to the profile at the points of maximum positive and negative slope
was taken as the approximate vessel diameter. For the data shown in Figure
2 the lumen diameter calculated on this basis was 5.0 mm while a direct
measurement of the vessel yielded a value of about 4 run. The profiles are
relatively symmetric and well developed and resemble profiles for laminar
oscillatory flow [3,12]. The profiles are drawn with straight line segments
connecting the velocity values at adjacent range locations and sharp dips or
peaks in the curves can result *rom slight variations in heart rate, cardiac
output or respiration during the time required to complete the vessel scan.
Figures 3 through 8 illustrate representative velocity waveforms and
profiles from the main, descending and circumflex branches of the left
coronary artery of a single pony. These data were obtained over a period
of about 30 minutes and during this time the pony's heart rate increased
from 60 beats/min to about 71 beats/min. Velocity waveforms in the main
branch at 7 equal spaced locations from the center of the vessel to the
far wall are shown in Figure 3. Again notice the decrease in mean velocity
during systole followed by a sustained forward velocity during diastole.
In this example an oscillation of 6 Hz is seen superimposed on the velocity
- 100 -
waveforms throughout the heart cycle and is particularly pronounced during
systole. Velocity profiles corresponding to these waveforms are given in
Figure 4. Successive profiles are off-set vertically by a distance equiva-
lent to a velocity increment of 2 cm/sec. From these records it appears
that the time varying velocity measured during systole at a distance of
3.1 mm is slightly elevated compared to the velocities at neighboring range
locations. Most probably, this artifact results from a momentary change in
cardiac output or arterial pressure or it may be associated with the induced
vibration of the vessel.
Velocity patterns from the near wall to the center of the descending
branch are shown in Figure 5. Generally, the waves are similar in shape
to waves in the main branch although the average velocities are somewhat
higher in the LAD because of its smaller diameter. Vessel diameters esti-
mated from the profiles were 6.4 mm for the main branch and 5.9 mm for the
descending branch. Profiles for the LAD are plotted in Figure 6.
The characteristic form of velocity waves in the circumflex branch
is markedly different from that in the main and LAD branches. Figure 7
illustrates the average velocity waveforms obtained in a scan of the
circumflex branch from the near wall to the center of the vessel. Veloc-
ity fluctuations resulting from the vibratory motion of the vessel are
again present during systole, however, their magnitudes are less than half
of the corresponding variations recorded from the main or LAD branch.
Furthermore these oscillations do not appear on the velocity waveforms
during diastole. With the exception of a transient cessation of the flow
at about t=500 msec, the mean forward velocity is about the same in systole
- 101 -
and diastole which Is also in contrast to the behavior noted for the other
two branches. Velocity profiles for the circumflex branch were constructed
from the measured waveforms and are shown plotted in Figure 8. The vessel
diameter for this example was estimated from the peak forward profile to
be 4.2 mm and was directly measured post-mortem as about 2 mm. Since the
length of the PUDVM sample volume is not small compared to the diameter of
this circumflex branch, the computed profiles may differ appreciably from
the true velocity distributions.
DISCUSSION
The blood velocity waveforms and profiles described above are repre-
sentative of the results obtained over the entire course of this study.
Except for the low frequency systolic fluctuations, the general character-
istics of the centerline velocities measured with the PUDVM are similar to
phasic flow waves recorded in the coronary arteries of dogs using electro-
magnetic or continuous wive Doppler flowmeters [13 -15]. Reynolds numbers
based on the peak centerline velocity normally ranged from about 300 to
600 in the major branches of the left coronary circuit although one flow
was observed for which the peak Reynolds number reached 1500 (cf. Fig. 1).
The unsteadiness parameter for the heart frequency was usually less than
4 which indicates that profiles corresponding to the mean phasic velocities
should be described by well developed boundary layer flows. On the other
hand, rapidly fluctuating local flows arising from the longitudinal vibra-
tions of the coronary branches were characterized by a values of 5 to 10
or more and relatively flat velocity profiles would be expected for these
- 102 -
flows. The calculated profiles illustrated above appear to support these
predictions. In general, the time varying profiles throughout systole
suggest that a plug-like flow occurs. during the period of most intense
velocity oscillations whereas more fully developed profiles appear later
in the flow cycle.
Velocity disturbances which would be indicative of transition or tur-
bulent flow cannot be detected on the velocity records because of the
limited frequency response of the PUDVM. Nerem and Seed [17] measured
velocities with a hot film anemometer in the ascending aorta of dogs and
found that flow disturbances generally occurred for values of ot>6 whenever
the peak Reynolds number exceeded about 150a. Even though the time his-
tories of the coronary and aortic flow pulse are markedly dissimilar only
entrance flow exists in either circuit. Furthermore, disturbances created
during the ejection of blood from the left ventricle could, under the proper
conditions, be transported into the coronary vessels as well as into the
aorta. Comparing Nerem's criteria for tne existence of flow disturbances
with the Reynolds numbers and frequency parameters corresponding to the
coronary flows described here leads to the conclusion that velocity dis-
turbances most probably would not be found in the major branches of the
left coronary artery.
The most critical question regarding pulsed Doppler velocity measure-
ments is instrument resolution. Since the PUDVM estimates velocity within
a finite sample region it is clear that the size of the sample region rela-
tive to the vessel dimensions ultimately determines the resolution and
accuracy of the measurements. A velocity profile obtained with the PUDVM
103-
is described analytically by a convolution of the sample region with the
actual velocity distribution [18] . The measured profile is broadened and
flattened by this convolution process and may also be distorted as a re-
sult of signal attenuation. In addition, since the PUDVM does not detect
zero velocity, the effective size of the sample region changes as it is
scanned across a vessel wall thereby introducing an additional boundary
error in the velocity estimate. In vessels which are sufficiently large
compared to the sample function the measured velocity profile may closely
approximate the true distribution. The NASA-PUDVM was used to estimate the
velocity profile for fully developed Poiseuille flow (Re - 1500) in a dialy-
sis tube 7.2 cm in diameter. Figure 9 compares the measured and predicted
profiles and indicates a slight broadening of the measured profile at the
far wall. The ultrasound beam passed through the center of the tube and
was inclined at an angle of 60 degrees to the flow axis. The scan diam-
eter estimated from the measured profile is in error by about 10%. The
convolution and boundary arrcrs severely li*it the accuracy of profiles
measured with the PUDVM in vessels with diameters less than about one-fourth
the length of the sample function [19]. For the PUDVM used in these studies,
calculated velocity profiles are expected to differ significantly in shape
from the true profiles in vessels less than 4 to 6 mm in diameter.
Although the PUDVM profiles may be distorted, it is possible to properly
account for the boundary error and compute the true time varying velocity
gradients at the wall. This calculation requires that one know a prio ri
the actual location of the wall on the estimated profile and this can be
obtained, for example, with an ultrasonic pulse-echo imaging system.
\
-104-
Although the correction factor does depend upon the shape of the sample
region and the true gradients, the measured profiles, in general, under-
estimate the velocity gradient at the wall by about one-half. From the
coronary profiles obtained in ponies the calculated maximum shear rates
were typically 400 to 600 J . In one instance (Fig. 2) the peak shear rate
reached about 3000 sec . The corresponding wall shear stresses are well
below the acute yield stress for endothelial cells of about 380 dynes/cm 2
suggested by Fry [1],
Perhaps the most interesting features of the coronary velocity patterns
reported here are the marked fluctuations which regularly occur during
systole. Measurements of coronary blood flow in dogs and man using electro-
magnetic or CW Doppler flowmeters [13-16,20] do not indicate the presence
of similar oscillations. Furthermore, the horse is not usually used for
studies of cardiovascular mechanics and there Is no Information In the
literature pertaining to either normal or abnormal coronary hemodynamic
patterns in t hi a species. - As sugges ted aLuve, these 5 to 10 Hz velocity
fluctuations appear to be generated as the artery vibrates along its axis.
The velocity signal then represents the superposition of the mean coronary
velocity with a locally induced velocity component associated with the
motion of the vessel. Relative to the transducer which is fixed to the
vessel, the induced flow has the characteristics of a piston-driven oscil-
lating flow in a rigid pipe where the relative velocity at the wall is
zero and the maximum velocity fluctuations occur in the center of the
vessel. This behavior is readily apparent from the measured velocity
waveforms in Figures 3,5, and 7. Momentarily occluding the vessel
-105-
i immediately adjacent to the transducer eliminated the induced velocity
(and the mean velocity also) as would be expected. In this case, the
vessel and blood must execute essentially the same motion in response to
the forced oscillation and no relative velocities develop. This situation
would be similar to a vibrating fluid-filled tube which is closed at both
ends. Other possible explanations for the genesis of these fluctuations
such as relative motion between the cuff and the vessel or twisting of
the flow cuff and vessel cannot be substantiated from the velocity records
or by direct visual observation. One might speculate that the occurrence
of these low frequency systolic vibrations is a species dependent phenomena.
It could be argued that in the dog, for example, analogous stress waves,
if generated, would be less intense and occur at a higher frequency com-
pared to the horse because of the dog's higher heart rate and lower cardiac
output. Furthermore, high frequency vibrations would be more rapidly damped
and perhaps not easily detected. Preliminary measurements obtained in our
laboratory of coronary velocity waves in a conscious intact horse also
indicate the presence of local flow fluctuations in the range of 5 to 10 Hz.
CONCLUSION
These results represent a first step toward quantifying the normal
hemodynamic patterns in coronary arteries. In the equine species, the
measured velocity waveforms are accented by low frequency fluctuations
apparently arising from the motion of the myocardial surface. The ampli-
tude of the induced velocity variation appears to depend upon the orienta-
tion of the vessel on the heart and may also vary during the cardiac cycle.
-106-
The significance of these oscillations relative to the development of
coronary artery disease or to the perfusion of the myocardium cannot be
evaluated on the basis of these initial observations. It is clear, how-
ever, that these unexpected local velocity patterns will greatly influence
the stability of the flow and the development of secondary and separated
flows and will have an important bearing on the consequences of cyclic
hydrodynamic forces.
ACKNOWLEDGEMENT
This work was supported by NSF grant GK41009. We acknowledge the
efforts of Dr. R. E. Daigle in developing the computer data reduction pro-
gram used in -these studies and thank Dr. J. F. Fessler, Visiting Professor
at Colorado State University and Professor of Large Animal Clinics at
Purdue University for his assistance in carrying out the experiments.
-107-
REFERENCES
1 Fry. D. L., "Acute Vascular Endothelial Changes Associated with
Increased Blood Velocity Gradients," Circulation Research , Vol . zz»
. 1968, p. 165.
2. Caro, C. G. , Fitz-Gerald, J. M., and Schroter, R. C. s "Atheroma and
Arterial Wall Shear: Observation, Correlation and Proposal of a
Shear Dependent Mass Transfer Mechanism for Atherogenesls , P rocee d-
ings of the Royal Society of London (B ), Vol. 177, 1971 , p. W*
3 Womerslev, J. R., "An Elastic Tube Theory of Pulse Transmission and
Oscillatory Flow in Mammalian Arteries," Wright Air Development Center,
Technical Report TR 56-614, 1957.
Ling, S. C., Atabek, H. G., Fry, D. L.. Patel, 0. J. and -Jantckl . J- S..
"Application of Heated-Film Velocity and Shear Probes to Hemodynamic
Studies," Circulation Research , Vol. 23, 1968, p. 789.
Seed, W. A., and Wood, N. B., "Development and Evaluation of^a Hot-
Film Velocity Probe for Cardiovascular Studies, Cardiovascular Re
search , Vol. 4, 1970, p. 253.
Nerem, R. M., Seed, W. A., and Wood, N. B , s tudy °f
the Velocity Distribution and Transition to Turbulence in the Aorta,
' Journal of Fluid Mechanics , Vol. 52, Part 1, 1972, p. 137.
Clark. C., and Shultz, U. L., "Velocity Distribution in Aortic Flow,"
Cardiovascular Research , Vol . 7 , 1973, p. 601.
4.
5.
6 .
7.
9.
10 .
8. Baker, D. W. , "Pulsed Ultrasonic uoppier bloou-Flow Sensing," IEEE;
Transactions on Sonics and Ultrasonics, , Vol. SU-17, 1970, p. 170.
Peronneau, P., Hinglais, J 4 , Pellet, M,, and Leger, F., “Vel ocl metre
Sanguin par Effet Doppler a Emission Ultrasonore Pulsee, L _ 0n de
Flectrigue , Vol. 50, 1970, p. 369.
Histand M B., Miller, C. W. , and McLeod, F. D., "Transcutaneous
Measurement of Blood Velocity Profiles and Flow," Cardiovascu l a r
Research , Vol. 7, 1973, p. 703.
n Morris R L. Histand, M. B., and Miller, C. W., "The Resolution of
the Ultrasound Pulsed Doppler for Blood Velocity Measurements,
Journal of Biomechanics , Vol. 6, 1973, p. 701.
12. Schlichting, H., Boundary Layer Theory , McGraw-Hill, New York, 1968.
13 Khouri, E. M. , Gregg, D. E., and Lowensohn, H. S., "Flow in the Major
Branches of the Left Coronary Artery During Experimental Coronary
Insufficiency in the Unanesthetized Dog," C j rc u 1 a t i on Re sea rch , Vol.
23, 1968, p. 99.
- 1 08 -
14. Hepps, S. A., Roe, B. B., and Rutkin, B. B., "Coronary Blood Flow
in the Intact Conscious Dog: Studies with Miniature Electromagnetic
Flow Transducers," Journal of Thoracic Cardiovascular Surgery , Vol.
46, 1963, p. 783.
15. Elliot, E. C., Khourl, E. M.., Snow, J. A., and Gregg, D. E., "Direct
Measurement of Coronary Collateral Blood Flow in Conscious Dogs by
an Electromagnetic Flowmeter," Circulation Research, Vol. 34* 1974,
p. 374.
16. Vatner, S. F., Franklin, D., Van Citters, L., and Braunwald, E.,
"Effects of Carotid Sinus Nerve Stimulation on the Coronary Circula-
tion of the Conscious Dog," Circulation Research , Vol. 27, 1970, p. 11.
17. Nerem, R. M. and Seed, W. A., "An In Vivo Study of Aortic Flow Dis-
turbances," Cardiovascular Researdu VoT. 6, 1972, p. 1.
18. Jorgensen, J. E., and Garbini, J. L., "An Analytical Procedure of
Calibration for the Pulsed Ultrasonic Doppler Flow Meter." Journal of
Fluids Enqineerinq, Transactions of the ASME, Vol. 96, Series 1, No. 2,
vmrpTlst —
19. Daigle, R. E., McLeod, F. D., Miller, C. W. , Histand, M. B., and Wells,
M. K., "Transcutaneous Measurement of Volume Blood Flow," Progress
Report on NASA Grant NSG-7009 prepared for the NASA-Ames Research
Center, 1974.
20. Benchemol , A., Stegall, H. F. , and Gartlan, J. L., "New Method to
Measure Phasic Coronary Blood Velocity In Man," American Heart Journal ,
Vol. 81, No. 1, 1971 . •>. 93 .
-109-
CAPTIONS
Figure 1.
Figure 2.
Figure 3.
Figure 4.
Figure 5.
Computer plot of one cycle of the average centerline velocity
waveform measured in the descending branch of the left coronary
artery of a pony. The beginning of the cycle coincides with
the R-wave of the electrocardiogram.
Calculated time varying velocity profiles in the horse LAD
coronary artery for 18 equally spaced time Intervals during an
average heart cycle, (a) The profile for t=0 sec is at the
bottom and subsequent profiles are plotted sequentially with a
10 cm/sec offset. The profile in the cycle having the maximum
average forward velocity is at the top. (b) Remaining profiles
beginning with the uppermost curve. The final profile of the
heart cycle is at the bottom.
Velocity waveforms measured in the main branch of the coronary
artery from the center of the vessel to the far wall. Near
wall to centerline velocities were also mapped. Nets the marked
6 Hz fluctuations during the first half of the cycle which may
be caused by vibrations of the artery.
Velocity profiles in the main branch constructed from the wave-
forms given in Figure 3. Profiles are offset by 2 cm/ sec for
clarity, (a) Profiles from t=0 to the time of peak forward
flow, (b) Subsequent profiles from peak forward flow to the
end of the heart cycle.
Velocity patterns across the near half of the descending branch
of the coronary artery. Corresponding velocity profiles are
shown in Figure 6.
- 110 -
Figure 6. (a) and (b). Estimated velocity profiles in the descending
branch. The profiles during the early part of the cycle appear
flattened compared to the later profiles which are more fully
developed.
Figure 7. Average velocity waveforms in the circumflex branch. The center-
line velocity oscillations during systole are only about half
the magnitude of the corresponding variations measured in the
main and descendina branches.
Figure 8. (a) and (b). Velocity profiles for the circumflex branch. Due
to the limited resolution of the PUDVM profiles calculated in
small vessels will be distorted especially near the walls and
in regions with high velocity gradients.
Figure 9. Velocity profile measured with the PUDVM compared to the pre-
dicted profile for Poiseuille flow in a 7.2 m diameter tube.
The ultrasound beam was inclined at 60 d«g to the tube axis.
-m-
T|*C IN*lLUSCC<*»
Figure 1 .
Figure 2
CENTER to r*B
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Figure 3.
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(b)
Figure 4
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Figure 9
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